Question

The automobile fuel called \(E 85\) consists of 85\(\%\) ethanol and 15\(\%\) gasoline. E85 can be used in the so-called flex-fuel vehicles (FFVs), which can use gasoline, ethanol, or a mix as fuels. Assume that gasoline consists of a mixture of octanes (different isomers of \(\mathrm{C}_{8} \mathrm{H}_{18} ),\) that the average heat of combustion of \(\mathrm{C}_{8} \mathrm{H}_{18}(l)\) is 5400 \(\mathrm{kJ} / \mathrm{mol}\) , and that gasoline has an average density of 0.70 \(\mathrm{g} / \mathrm{mL}\) . The density of ethanol is 0.79 \(\mathrm{g} / \mathrm{mL}\) . (a) By using the information given as well as data in Appendix \(\mathrm{C},\) compare the energy produced by combustion of 1.0 L of gasoline and of 1.0 . of ethanol. (b) Assume that the density and heat of combustion of E85 can be obtained by using 85\(\%\) of the values for ethanol and 15\(\%\) of the values for gasoline. How much energy could be released by the combustion of 1.0 L of E85? (\mathbf{c} ) How many gallons of E85 would be needed to provide the same energy as 10 gal of gasoline? (d) If gasoline costs \(\$ 3.88\) per gallon in the United States, what is the break- even price per gallon of E85 if the same amount of energy is to be delivered?

Short answer

The energy released by combustion of 1.0 L of gasoline is 33156 kJ, whereas 1.0 L of ethanol releases 23502 kJ. Combustion of 1.0 L of E85 mixture releases 24950.3 kJ. To provide the same amount of energy as 10 gallons of gasoline, 50.3 gallons of E85 would be needed. The break-even price per gallon of E85 is $0.771.

Step-by-step solution

Calculate the energy produced by 1.0 L of gasoline

First, we will need to find the number of moles of gasoline in 1.0 L: 1.0 L gasoline × (1000 mL / 1 L) × (0.70 g / mL) = 700 g of gasoline In order to find the moles, we have to divide the mass by the molar mass (114 g/mol for octane, which is C8H18) of gasoline: (700 g) / (114 g/mol) = 6.14 mol of gasoline Now, we can use the heat of combustion (ΔH) value given for gasoline (5400 kJ/mol) to find the energy released by 1.0 L of gasoline: (6.14 mol) × (5400 kJ/mol) = 33156 kJ

Calculate the energy produced by 1.0 L of ethanol

Similar to gasoline, we will need to find the moles of ethanol in 1.0 L: 1.0 L ethanol × (1000 mL / 1 L) × (0.79 g / mL) = 790 g of ethanol The molar mass of ethanol (C2H5OH) is 46 g/mol. So we have: (790 g) / (46 g/mol) = 17.2 mol of ethanol The heat of combustion for ethanol (ΔH) is -1367 kJ/mol, which can be found in the appendix provided by the question. We can find the energy released by 1.0 L of ethanol: (17.2 mol) × (-1367 kJ/mol) = 23502 kJ

Calculate the energy produced by 1.0 L of E85

We assume that 85% ethanol and 15% gasoline contribute to the E85 values. Calculate the energy released by 1.0 L of E85: 0.85 × 23502 kJ (from ethanol) + 0.15 × 33156 kJ (from gasoline) = 19976.9 kJ + 4973.4 kJ = 24950.3 kJ

Calculate the gallons of E85 needed to provide the same energy as 10 gallons of gasoline

First, find the energy delivered by 10 gallons of gasoline: 10 gal × 3.785 L/gal × 33156 kJ/L = 1255927 kJ Now, we want to find how many gallons of E85 are needed to provide this energy: (1255927 kJ) / (24950.3 kJ/gal) = 50.3 gal

Calculate the break-even price per gallon of E85

Find the cost of 10 gallons of gasoline: 10 gal × \(3.88/gal = \)38.80 Divide the cost of 10 gallons of gasoline by the number of gallons of E85 needed to deliver the same energy: (\(38.80) / (50.3 gal) = \)0.771/gal The break-even price per gallon of E85 is $0.771.

Key concepts

Energy Content of Fuels

The energy content of a fuel is a crucial measure that indicates the amount of energy that can be harnessed from burning a specified amount of that fuel. This is typically expressed in units like kilojoules per mole (kJ/mol) for chemical amounts, or in kilojoules per liter (kJ/L) for liquid fuels. Understanding the energy content helps us compare different fuels, such as ethanol and gasoline, which have differing chemical compositions and thus release different amounts of energy upon combustion.

For instance, in a classroom scenario, students might be asked to calculate the energy produced by combusting 1.0 L of gasoline compared to 1.0 L of ethanol. This involves determining the number of moles in one liter of each fuel using their densities and molar masses, and then using the heat of combustion to calculate the total energy output. Such exercises illustrate the direct relationship between the energy content of a fuel and its chemical properties, and why this information is instrumental for applications like automotive engineering and environmental management where fuel efficiency and emissions are critical.

Flex-Fuel Vehicles

Flex-fuel vehicles (FFVs) can operate on more than one type of fuel and typically run on mixtures of gasoline and ethanol, like E85, which contains 85% ethanol. FFVs are designed with a flexible fuel system that can adjust to different fuel compositions, allowing the engines to optimize the burn process for various blends. This adaptability helps reduce dependence on pure gasoline and contributes to a reduction in greenhouse gas emissions, as ethanol is a renewable biofuel that results in lower carbon emissions than traditional gasoline.

Students studying FFVs might evaluate the energy produced by different fuel blends to understand the economic and environmental impacts. A common exercise involves calculating the energy release from burning 1.0 L of a flex-fuel like E85, with the understanding that its properties can be approximated by considering it as 85% ethanol and 15% gasoline. This understanding provides insight into energy policies and decisions around fuel standards and vehicle design.

Combustion Reactions

Combustion reactions are exothermic chemical processes where a fuel and an oxidant (typically oxygen) react to produce heat and combustion products such as CO2 and water. The energy released during combustion is harnessed for various uses, like powering vehicles or generating electricity. The amount of energy released during these reactions can be calculated through heats of combustion, which are experimentally determined values representing the energy change when one mole of a substance burns completely.

In an educational setting, this concept may be brought to life by solving problems showing students how to calculate the energy yielded from the combustion of different fuels. For example, the heat of combustion is used to evaluate how many gallons of E85 are required to match the energy from a certain number of gallons of gasoline. These comparisons illustrate the fundamental principles of stoichiometry and thermochemistry, underlining combustion reactions' role in energy production and consumption in our daily lives.